Geometry of coplanar stereoscopic radiographic pairs for analysis of the lateral cervical radiograph: a study using mathematical models

ObjectiveThis study evaluated 3-dimensional (3D) assessments of points of interest on a phantom replica of the human skull and cervical vertebrae to better understand how structures are represented in space using mathematical methods.MethodsThree basic geometric equations derived from the “Law of Similar Triangles” are introduced, and measurements are taken after 4 trials to demonstrate how 3D data extracted from 2-dimensional (2D) digitized radiographic pairs can be used to produce coordinate points associated with 3 areas on the atlas.ResultsAn analysis of variance test for multiple group comparison shows no significant statistical difference between 4 trials (P = 0.995). In addition, 6 strong positive correlations are evident using Pearson product-moment coefficient test (r = 0.9008 through 0.9977, P = 0.002).ConclusionThis study suggests that it is possible to use coplanar stereoscopic radiographic pairs to define an object's location in 3D space by taking retrospective measurements directly from 2D digitized radiographs.